Rodent carcinogenicity experiments are commonly used to screen environmental chemicals, drugs and food additives for carcinogenic potential. Animals are assigned to either a control group or a dose level of the substance, and examined at predetermined sacrifice or at natural death for the development of various tumor types. The statistical analysis of these experiments involves three aspects: 1) testing for dose group differences in the rate of tumor development, 2) estimation of the carcinogenic potency, or magnitude of the dose effect, and 3) assessment of risk at very low doses which represent potential human exposure, by extrapolation down from the much higher experimental doses administered to animals. The analysis of these experiments must appropriately deal with the following issues: 1) although the comparison of interest is the time to tumor onset, this event is not directly observable; 2) dose group differences in non-tumor mortality can potentially bias the analysis; 3) there are often several tumor sites examined on each animal; and 4) although the experiment is conducted at high dose levels in rodents to guarantee the development of some tumors, interest is focused on the lifetime risk of low dose exposure for humans. The goal of this proposed research is the development of methods of testing for, and estimating the carcinogenic potential of substances, which appropriately accounts for these issues. This research will result in a statistical test and estimate of the overall effect of a substance on the rate of development of tumors at several sites. Furthermore, the methodology will be applied to the problem of low-dose extrapolation to obtain an estimate of the lifetime risk of tumor which is corrected for dose-related non-tumor mortality. The methodology will be extensively tested using the data from the ED01 experiment as well as computer simulations.